Evaluate the Integral integral of 2t with respect to t

Problem

(∫_^)(2*t*d(t))

Solution

1. Identify the integrand and the variable of integration. The integrand is 2*t and the variable is t

2. Apply the constant multiple rule for integration, which allows the constant 2 to be moved outside the integral.

(∫_^)(2*t*d(t))=2*(∫_^)(t*d(t))

3. Apply the power rule for integration, which states that (∫_^)(tn*d(t))=(t(n+1))/(n+1) for n≠−1 Here, n=1

2*(∫_^)(t1*d(t))=2⋅(t(1+1))/(1+1)

4. Simplify the expression by performing the arithmetic in the exponent and the denominator.

2⋅(t2)/2

5. Cancel the common factor of 2 and add the constant of integration C

t2+C

Final Answer

(∫_^)(2*t*d(t))=t2+C

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